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Singly reinforced rectangular beam

K-method design of a rectangular beam with the rectangular stress block, lever arm and tension steel. Reference: EN 1992-1-1 3.1.7, 5.6.3, 6.1.

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Singly reinforced rectangular beam: worked example sheet in Equation Pad with typeset equations and results.

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# Materials
f_ck := 30 MPa
f_yk := 500 MPa
gamma_c := 1.5
gamma_s := 1.15
alpha_cc := 1.0
f_cd := alpha_cc*f_ck/gamma_c =
f_yd := f_yk/gamma_s =

# Section and action
b := 300 mm
d := 500 mm
M_Ed := 220 kN*m

# Design
K := M_Ed/(b*d^2*f_ck) =
k_1 := 0.8*alpha_cc/gamma_c =
xi_lim := 0.45
K_lim := k_1/0.4*(1 - 0.4*xi_lim)*0.4*xi_lim =
K <= K_lim =
z := min(d*(0.5 + sqrt(0.25 - 0.4*K/k_1)), 0.95*d) = mm
A_s := M_Ed/(f_yd*z) = mm^2
A_s.min := max(0.26*0.30*(f_ck/(1 MPa))^(2/3)*1 MPa/f_yk, 0.0013)*b*d = mm^2
A_s.max := 0.04*b*550 mm = mm^2

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